Particle in a

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Particle in a box Quantum Dots

• Quantum dots, or fluorescent semiconductor
  nanocrystals, are revolutionizing biological
  imaging.

The color of light emitted by a semiconductor
material is determined by the width of the energy
gap separating the conduction and valence energy
bands.
In bulk semiconductors, this gap width is fixed
by the identity (i.e. composition) of the
material. For example, the band gap energy of
bulk CdSe is 1.77 eV at 300 K.
2

• Recall that a photon obeys
• for the relationship between the energy gap and
  the frequency or wavelength

If you want a different wavelength of light to be
emitted, you need to find a different material.
However, the situation changes in the case of
nanoscale semiconductor particles with sizes
smaller than 10 nm. This size range corresponds
to the regime of quantum confinement, for which
the spatial extent of the electronic wavefunction
is comparable with the dot size.
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• As a result of these geometrical constraints,
  electrons respond to changes in particle size by
  adjusting their energy. This phenomenon is called
  the quantum size effect.

The quantum size effect can be approximately
described by the particle in a box model. How
good is this approximation? Good see Weber,
Phys. Rev. B, 66 041305 (2002).
For a spherical quantum dot with radius R, this
model predicts a size-dependent contribution to
the energy gap proportional to 1/R2. Hence the
gap increases as the quantum dot size decreases.